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FRM Part II · FRM Exam Part II · Backtesting VaR

A bank uses a 99% one-day VaR model and tests it with a two-sided binomial test at the 5% significance level over a long sample. The model produces far fewer exceptions than expected, for example 0 exceptions in 500 days. What is the most appropriate conclusion?

The model may be rejected as too conservative. Zero exceptions in 500 days has a probability of about 0.7% when 5 are expected, so a two-sided test rejects it. This indicates VaR is overstated, leading to inefficient capital use, rather than understated risk.

  1. AThe model is accepted because too few exceptions is always conservative and costless
  2. BThe model may be rejected as overly conservative, since the exception count is statistically too low, implying capital is inefficiently heldCorrect
  3. CThe model must be rejected because it understates risk
  4. DThe test is invalid because exceptions cannot be zero

Explanation

With 500 days and p = 1%, expected exceptions are 5, and the probability of 0 is 0.99^500, about 0.7%, which is very low. A two-sided test therefore rejects, signalling overestimated VaR and excessive capital, not understatement of risk.

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